Saturday, March 8, 2014

Teaching Math 5H: UNIT 8 Advanced Integration Techniques

We didn't get very far this past couple of weeks with all the Snow Days and February Break! We did manage to cover most of UNIT 8 about Integration By Parts and Partial Fractions. We started the unit with a class on L'Hopital's rule using the "Mean Girls Limit" as a Do Now! I also ended that class with a Calculus Carol by one of my students about L'Hopital as a summary. I do this topic now as these limits will start to become an issue soon!

I will finish the unit next week with a discussion of Variable Separable DiffEqus including Logistics, Slope Fields and Euler's Method.

UNIT 8 Advanced Integration Techniques:

Quarter III Weeks 1&2: 2/3-2/14

We didn't get very far this past couple of weeks with 3 SnowDays and a Delayed Opening in the way! We did somehow manage to finish UNIT 7 focusing on Differential Equations. We talked about Slope Field and Variable Separable solutions for Exponential Growth and Decay, Exponential Approach (aka Newton's Laws of Heating or Cooling) and Logistic Growth models! After February Break we have our last AB Part I MCQ Monday and then we'll talk about L'Hopital's Rule and Indeterminate Forms.

Announcement from the AP Calculus Forum:

FREE! MOOC style AP Review courses at coursera.com only for Calc and Stats at present!

The University of Houston is offering the following FREE courses through Coursera, with start dates of March 17. Registration is currently taking place. Please inform your interested students and colleagues.

Quarter II Weeks 8&9: 1/13-1/24

We started UNIT7: Transcendental Functions! We focused on the derivative of ln(x) and Logarithmic Differentiation. Next week and after Midterm Week, we'll revisit Applications of Derivatives, Applications of Integrals and Variable Separable Differential Equations involving e^x and ln(x).

UNIT 7 Calculus of Transcendental Functions:

Quarter II Week 7: 1/6-1/10

We finished UNIT6: Applications of the AntiDerivative! We focused on Volumes with Known Cross Sections, Arc Length and Surface Area.

Quarter II Week 6: 12/16-12/20

We continued UNIT6: Applications of the AntiDerivative! We focused on Volumes of Revolution with horizontal and vertical strips: Disk, Washer, Shell. Of course, Friday was Calculus Caroling Day!

Quarter II Weeks 4&5: 12/2-12/13

We started UNIT6: Applications of the AntiDerivative! We focused on the Betty Sue problem and the importance of adding a constant C. We talked about horizontal and vertical strips in our Riemann Statements for finding area between curves and Volumes of Revolution.

UNIT 6 Applications of AntiDerivatives:

Quarter II Week 3: 11/25-11/29

This week we continued our discussion of AntiDerivatives by introducing The Fundamental Theorem Parts I and II! We went over a MCQ Monday on Monday and did the Fundamental Theorem on Tuesday. This was a short week due to Thanksgiving, so we had GAMEDAY on Wednesday. Fun was had by all!

Since we were covering Indefinite Integrals this week, we had to do the Betty Sue FRQ and sing the song!

Also, next week is December already, so we start practising our preCalculus and Calculus Carols!

Quarter II Week 2: 11/18-11/22

This week we continued our discussion of AntiDerivatives and Riemann Sums! We focused on Scientific Computing. IE: we wrote programs in TI89 BASIC demostrating the Numerical Methods for definite integration: LSUM, RSUM, MSUM, TRAP and SIMP!

Quarter II Week 1: 11/11-11/15

This week was all about AntiDerivatives and Riemann Sums! We talked about Right Riemann Sums as exact limits. Next week we'll have to right some TI89 code! We also started talking about solving Variable Separable Differential Equations.

UNIT 5 AntiDerivatives and Riemann Sums:

Quarter I Week 9: 11/4-11/8

We finally finished with UNIT 4: Application of Differentiation this week. We programmed Newton's Method in TI89-BASIC. We also covered related rates. Next week is all about AntiDerivatives and Reimann Sums!

Quarter I Week 8: 10/28-11/1

We're nearly finished with UNIT 4: Application of Differentiation this week. We programmed Newton's Method in TI89-BASIC. We also started related rates this week.

Quarter I Week 7: 10/21-10/25

We started UNIT 4: Application of Differentiation this week. We started talking about IVT, MVT, Min/Max and Optimization!

UNIT 4 Applications of Derivatives:

Quarter I Week 6: 10/14-10/18

This week we finished UNIT 3 with a discussion of the Chain Rule, Implicit Differentiation, Min/Max and Related Rates.

Quarter I Week 5: 10/07-10/11

Out sick.... However, I did start using DropBox, see above!

Quarter I Week 4: 9/30-10/04

We started UNIT 3 about Differentiation! We derived the Product and Quotient Rules. We did all 6 Trig Rules. We started talking about the Chain Rule.

UNIT 3 Differentiation Rules:

Quarter I Week 3: 9/23-9/27

We finished UNIT 2 with a test! Our last topic concerned the existence of the derivative. BTW, we start with UNIT 2 since UNIT 1 is just a review of PreCalculus. We did a bit of that in 106 and 107 on Conics and Polar Notation.

Quarter I Week 2: 9/16-9/20

We are almost finished with UNIT 2: Continuity and Differentiablility! We demostrated the Power Rule using the Definition of the Derivative as the limit of the Difference Quotient. We even started the Trig Rules!

Quarter I Week 1: 9/9-9/13

AP Calculus BC started with a preCalc review in the form of the topic of Conic Sections! This is a great topic to review Cartesian and Polar Coordinates, as well as some algebra, trig and TI89 usage!

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The Calculus & Computer Science Archive ProjectOnline Since 1988

This site is here to help new and experienced teachers alike. Over the years I have developed many materials for several courses that I teach regularly. I have taught AP Computer Science since 1987, College Math since Fall 1993 and AP Calculus since 1994.

These materials have been edited and re-edited for ease of use in the classroom every time I have a chance to teach these courses. I have had many requests to share my materials at the conferences I frequent, whence this website.